# Find temperature change required

1. Apr 28, 2014

### utkarshakash

1. The problem statement, all variables and given/known data
A smooth vertical tube having two different sections is open from both ends equipped with two pistons of different areas figure. Each piston slides within a respective tube section. One mole of ideal gas is enclosed between the pistons tied with a nonstretchable thread. The cross-sectional area of the upper piston is ΔS greater than that of the lower one. The combined mass of the two pistons is equal to m. The outside air pressure is P0. By how many Kelvin’s must the gas between the pistons be heated to shift the pistons through l?

2. Relevant equations
http://www.luiseduardo.com.br/mechanics/liquids/liquidsproblems_arquivos/image028.jpg [Broken]

3. The attempt at a solution

Pressure of gas present inside = P0 + mg/ΔS

I have a doubt regarding the pressure of the gas. Will it remain the same throughout the expansion? If yes, why?

Last edited by a moderator: May 6, 2017
2. Apr 28, 2014

### Staff: Mentor

You don't have to worry about the expansion process, it is sufficient to consider the situation in equilibrium - and there, your formula is valid independent of the expansion that happened.

3. Apr 28, 2014

### utkarshakash

What if the two pistons were connected by an ideal spring?

4. Apr 28, 2014

### SammyS

Staff Emeritus
That seems like a reasonable concern to have.

What pressure is required for this system to remain at a given level ?

Last edited by a moderator: May 6, 2017
5. Apr 28, 2014

### utkarshakash

Since the process is quasi-static, the pressure inside must remain same at all times. Am I correct?

6. Apr 28, 2014

### SammyS

Staff Emeritus
I didn't notice the equation:
Pressure of gas present inside = P0 + mg/ΔS​
.

That pretty much says that the pressure is the same after pistons move.

7. Apr 29, 2014

### Staff: Mentor

Then you have a completely different problem.

8. Apr 30, 2014

### utkarshakash

$ΔT = \left( ΔP + \frac{mg}{ΔS} \right) ΔS l$